Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

/pdf/collective-dynamics-of-small-world-networks-205zhem3gm.pdf

Collective dynamics of small-world networks

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Publisher Summary This chapter focuses on the modern notion of short-term memory, called working memory. Working memory refers to the temporary maintenance of information that was just experienced or just retrieved from long-term memory but no longer exists in the external environment. These internal representations are short-lived, but can be maintained for longer periods of time through active rehearsal strategies, and can be subjected to various operations that manipulate the information in such a way that makes it useful for goal-directed behavior. Working memory is a system that is critically important in cognition and seems necessary in the course of performing many other cognitive functions, such as reasoning, language comprehension, planning, and spatial processing. This chapter demonstrates the functional importance of dopamine to working memory function in several ways. Elucidation of the cognitive and neural mechanisms underlying human working memory is an important focus of cognitive neuroscience and neurology for much of the past decade. One conclusion that arises from research is that working memory, a faculty that enables temporary storage and manipulation of information in the service of behavioral goals, can be viewed as neither a unitary, nor a dedicated system. Data from numerous neuropsychological and neurophysiological studies in animals and humans demonstrates that a network of brain regions, including the prefrontal cortex, is critical for the active maintenance of internal representations.

Chapter 11 Working memory

Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Complex brain networks: graph theoretical analysis of structural and functional systems

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

A FUNDAMENTAL step in visual pattern recognition is the establishment of relations between spatially separate features. Recently, we have shown that neurons in the cat visual cortex have oscillatory responses in the range 40–60 Hz (refs 1,2) which occur in synchrony for cells in a functional column and are tightly correlated with a local oscillatory field potential. This led us to hypothesize that the synchronization of oscillatory responses of spatially distributed, feature selective cells might be a way to establish relations between features in different parts of the visual field2,3. In support of this hypothesis, we demonstrate here that neurons in spatially separate columns can synchronize their oscillatory responses. The synchronization has, on average, no phase difference, depends on the spatial separation and the orientation preference of the cells and is influenced by global stimulus properties.

Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties.

Classical theories of sensory processing view the brain as a passive, stimulus-driven device. By contrast, more recent approaches emphasize the constructive nature of perception, viewing it as an active and highly selective process. Indeed, there is ample evidence that the processing of stimuli is controlled by top-down influences that strongly shape the intrinsic dynamics of thalamocortical networks and constantly create predictions about forthcoming sensory events. We discuss recent experiments indicating that such predictions might be embodied in the temporal structure of both stimulus-evoked and ongoing activity, and that synchronous oscillations are particularly important in this process. Coherence among subthreshold membrane potential fluctuations could be exploited to express selective functional relationships during states of expectancy or attention, and these dynamic patterns could allow the grouping and selection of distributed neuronal responses for further processing.

/pdf/dynamic-predictions-oscillations-and-synchrony-in-top-down-g571k2ka9j.pdf

Dynamic predictions: Oscillations and synchrony in top–down processing

The mammalian visual system is endowed with a nearly infinite capacity for the recognition of patterns and objects. To have acquired this capability the visual system must have solved what is a fundamentally combinatorial prob­ lem. Any given image consists of a collection of features, consisting of local contrast borders of luminance and wavelength, distributed across the visual field. For one to detect and recognize an object within a scene, the features comprising the object must be identified and segregated from those comprising other objects. This problem is inherently difficult to solve because of the combinatorial nature of visual images. To appreciate this point, consider a simple local feature such as a small vertically oriented line segment placed within a fixed location of the visual field. When combined with other line segments, this feature can form a nearly infinite number of geometrical objects. Any one of these objects may coexist with an equally large number of other

Visual feature integration and the temporal correlation hypothesis

In areas 17 and 18 of the cat visual cortex the firing probability of neurons, in response to the presentation of optimally aligned light bars within their receptive field, oscillates with a peak frequency near 40 Hz. The neuronal firing pattern is tightly correlated with the phase and amplitude of an oscillatory local field potential recorded through the same electrode. The amplitude of the local field-potential oscillations are maximal in response to stimuli that match the orientation and direction preference of the local cluster of neurons. Single and multiunit recordings from the dorsal lateral geniculate nucleus of the thalamus showed no evidence of oscillations of the neuronal firing probability in the range of 20-70 Hz. The results demonstrate that local neuronal populations in the visual cortex engage in stimulus-specific synchronous oscillations resulting from an intracortical mechanism. The oscillatory responses may provide a general mechanism by which activity patterns in spatially separate regions of the cortex are temporally coordinated.

https://www.pnas.org/content/pnas/86/5/1698.full.pdf

Wolf Singer

Papers

Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties.

Dynamic predictions: Oscillations and synchrony in top–down processing

Visual feature integration and the temporal correlation hypothesis

Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex

Neuronal Synchrony: A Versatile Code for the Definition of Relations?